A Stochastic or random process is a term used in probability theory and is the opposite of a deterministic process. Deterministic events and procedures do not exist. The Universe speaks to us in the language of probability theory. The word stochastic(the Greek word meaning “to aim at a mark, guess”) in English initially used as an adjective with the definition “about conjecturing.
One of many realities
Instead of dealing only with one possible “reality” of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. It means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. Due to its randomness.
The term random function used to refer to a stochastic or random process, though sometimes it is only used when the stochastic process takes real values. It is a collection of random variables that are indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the game. The collection is called the index set. A single outcome of a stochastic process is called a sample function or realization. If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes, respectively referred to as discrete-time and continuous-time stochastic processes.
sources and useful information
- Stochastic World by Sergey S. Stepanov. Published 2013 by Springer